Answer:
x = 15 or x = - 
Step-by-step explanation:
Cross- multiplying gives
(14x + 6)(17x + 5) = 9x(27x + 11) ( expanding factors )
238x² + 172x + 30 = 243x² + 99x
rearrange into standard form : ax² + bx + c = 0
5x² - 73x - 30 = 0 ← in standard form
consider the factors of the product 5 × - 30 = - 150 which sum to the coefficient of the x-term (- 73 )
the factors are - 75 and + 2
Use these factors to split the middle term
5x² - 75x + 2x - 30 = 0 ( factor by grouping )
5x(x - 15) + 2(x - 15) = 0 ← take out the factor (x - 15)
(x - 15)(5x + 2) = 0
equate each factor to zero and solve for x
x - 15 = 0 ⇒ x = 15
5x + 2 = 0 ⇒ x = - 
Answer:
11
Step-by-step explanation:
5x+15+20=90
5x+35=90
-35 from both sides
5x=55
divide both sides by 5
x=11
8.4444 i think I’m not sure
Answer:
P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Step-by-step explanation:
Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3
Basis: P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:
2(k+1) - 1 = 2k + 2 - 1
≤ 2 + k! (by the inductive hypothesis)
= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.
I think the answer is 160, I'm not completely sure. Anyway, have a good day!